(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Biodiversity Heritage Library | Children's Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Scientific Papers - Vi"

1918]       ON THE DISPERSAL OF  LIGHT BY  A DIELECTRIC  CYLINDER
561
As might have been expected, the modulus, representing the amplitude of vibration, is greater in the second case, that is in the direction of the primary ray produced.
For other angles, except 90, the calculation is longer on account of the factor cos m&. The angles chosen as about sufficient are 0, 30, 60, 90 and their supplements. For 2 or 3 of the larger z's the angle 45 and its supplement were added. The results are embodied in Table II, and a plot of most of them is given in Fig. 1, where the abscissa is the angle 0 and the ordinate the corresponding modulus from the table. The curve marked N corresponds to (22) and that marked N' to (26). A few points have been derived from values not tabulated. From the nature of the functions represented both curves are horizontal at the limits 0 and 180.
When z = '8, the curves show the characteristics of a very thin cylinder. At 90 N' nearly vanishes, indicating that in this direction little light is scattered whose vibrations are perpendicular to the axis. When z= T2, the maximum polarization is still pretty complete, but the direction in which it occurs is at a smaller angle d. For z  T6 the polarization is reversed over most of the range between 45 and 90. By the time z has risen to 2'4> a good deal of complication enters, at any rate for the curve N.
TABLE II.
6	[ 3 in (22)	Modulus	[ ] in (2G)	Modulus
0	10222 -ix '01823	1038	- -05808 + ix -00295	0582
30	1027-5 -tx '01 824	1044	- '05048 + 1 x -00255	0505
60	10421 -ix -01824	1058	- -02925 + tx -00147	0293
90	10622- i x -01825	1078	+ -00080 -ix -00001	0008
120 '	10825 -i x -01826	1098	03207 -tx -001 49	0321
150	10975 -ix '01826	1113	05574- ix -00257	0558
180	1 1030- ix -01827	1118	06456 - 1 x -00297	0646
e	[ 1 in (22)	Modulus	[  ]in{26)	Modulus
0	22476 -ix 18576	2916	- -16535 + ix O3618	1693
30	23303-ix -18625	2983	~ -14502 -H'x -031 19	1483
60	25625 -ix '18768	3176	- -08356 + ix -01746	0854
90	28936- tx -18940	3458	+ -01 535 -ix -00154	0154
120	32415 -ix '19122	3763	13288- ix -02082	1345
150	36071 -ix -19255	4001	231 58 -.ix -03511	2342
180	36068-ix -19304	4091	27053 -ix -04038	2735
R. VI.
36) must be taken with the opposite sign from (18) of  341.   W. P. S.] J Reports for 1913, p. 115; 1914, p. 75. also agreesion.again, as in (1), so that the vibration is A sin2 6 + C cos2 6, reducing to G simply, if A = G. This is the result for a single particle whose axis is at W. What we are aiming